The best possible dielectric from a loss standpoint is a vacuum. Unfortunately, the requirements for creating and sustaining vacuums in signal carrying conductors presents a mechanical problem for production and installation, since the impedance is also affected by the geometry of the conductors and shields. The manufacturers that make the cables I've seen claim that the battery is somehow used to charge the shield, and in doing so attempt to polarize the dielectric, with the claim that this somehow lowers the noise floor of the cable.
Voltage by definition is a difference in potential, and in this case the reference point is the opposite unterminated contact of the power source, rather than the signal carrying contact. Charge carriers are supposed to drift out of the power source into the shield (through mutual repulsion I guess), without actual current flow (other than leakage through the air gap between the unterminated source and the connection to the shield).
In other designs, I would guess that the return point is another shield, causing a difference of potential between them, but again no current flow (other than leakage through the dielectric). In either case, CharlyD has it dead on, a polarized dielectric between charged conductors constitutes a capacitor, and if it moves it changes voltage potential, and generates spurious noise input.
The best possible shield is one that exhibits as close to ZERO impedance as possible, and is as at close to ground potential as possible. If using balanced conductors (length and geometry identical as near as possible) then the most of the crap coming in will be shunted to ground through the low shield impedance. Any common mode crap that makes it past the shield will be differenced in the differential input. The rest of this ought to be minimize the losses and minimize the impedance mismatch between source and load so that power is not converted to reflections in the applied signal. I do not know how much of this is used or (AB)used by cable manufacturers, but I have often wondered why contact impedance is not controlled better in equipment and cables.
Originally Posted by rolexdaytona
Someone already sells a cable with a battery giving juice to the shield.